Process Batch Fingerprint
All perfectly replicated systems have the same PBF

This figure, copied from the Process Variable Analyzer section is the time evolution of the process batch "Hot Water." It was done in March, as shown in the date fields on top. This is a very simple fingerprint, a PBF that is simply a trace of temperature of a Hot Water - under specific conditions.
Simple, yes. But is it the correct way to make Hot Water?

Now look at this PBF. It is a "Hot Water" process batch done in January, the way Hot Water is supposed to be made. It is the standard against which all future batches of Hot Water are matched. The March traces do not look like these. The PBFs do not match.
You can easily conclude that the March batch was not made properly.
Not only is it clear that the March batch has been made incorrectly, even a casual observation shows what is different: the operator did at least two things wrong.
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The March batch started out too hot by 10C.
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The dowsing with cold water two minutes after the start, was skipped in March.
The PBF technique is straightforward and intuitive. It shows the various traces of all the relevant parameters that go into a batch product and the results of what happens inside the batch as measured with a specific set of real and virtual analyzers.
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Inputs to the batch include material additions or energy additions steam heat or agitator speeds.
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Results inside the batch include the color, amount of particulates or energy needed to move agitators.
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Most commonly PBFs are traces of the time evolution of one or more of the material or energy parameters.
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But intra-parameter PBFs such as the power needed versus temperature are also informative.
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A real manufacturing process is fully described by a trace of all the parameters versus time, the Total PBF. While often difficult to interpret, the Total PBF can be broken down into smaller, simpler units called Elemental PBFs.
No matter how many items you have going on at the same time - and with heat, agitation, ingredients, vacuum there can be startlingly many as shown in OmniBatch - all batches systems are characterized by their PBF.